A particle executes simple harmonic motion of ampliltude A. At what distance from the mean position is its kinetic energy equal to its potential energy?

Explanation

The P.E. at a distance `y = (1)/(2)momega^(2)y^(2) = E_(p)`
K.E. at a distance ` y = (1)/(2) momega^(2)(a^(2) - y^(2)) = E_(x)`
As `E_(p) = E_(k)`
`(1)/(2)momega^(2)y^(2) = (1)/(2)momega^(2)(a^(2) - y^(2))`
` (1)/(2)momega^(2)y^(2) + (1)/(2)momega^(2)y^(2) = (1)/(2)momega^(2)a^(2)`
` 2y^(2) = a^(2)`
` y = (a)/(sqrt(2))`